Two planes are flying at the height of 10-km. They are going at the same speed, and both traveling due north. If the planes are 3,000 km apart as measured along the surface of the earth, what angle do the lines from the planes make to the center of the Earth make?

Question

Two planes are flying at the height of 10-km.  They are going at the same speed, and both traveling due north.  If the planes are 3,000 km apart as measured along the surface of the earth, what angle do the lines from the planes make to the center of the Earth make?

Steve · Answer

You can see that the altitude of the planes makes no difference. If the earth is considered a sphere with a polar radius of 6357 km, then an arc of 3000 km subtends an angle of 3000/(2pi*6357) radians